Chapter 3 - Smart Work

Find the median for the following sample of data: 8, 3, 6, 6, 4, 8, 8, 7. Multiple choice question. 5 6.5 6.25 8

6.5

Calculate the mean of the following sample of data: 12, 15, 6, 4, 8. Multiple choice question. 8 11 4 9

9

Calculate the mean of the following sample of data: 12, 4, 6, 6. Multiple choice question. 7 8 6 4 12

Correct Answer 7 find as 12+4+6+6=28 28/4=7

Calculate the mean of the following sample of data: 12, 15, 6, 4, 8. Multiple choice question. 15 11 8 4 9

Correct Answer 9

What is the definition of "parameter"? Multiple choice question. A characteristic of a sample A characteristic of a population. A characteristic of the middle 50% of a population.

Correct Answer A characteristic of a population.

The mode can be computed for which of the following levels of data?

Correct Answer Nominal Ordinal

Which of the following kinds of data can be used to find a median value?

Correct Answer Ratio level data Interval level data Ordinal level data

Why would the median be a better measure of the center than the mean for the following set of data? 3, 4, 4, 4, 5, 6, 7, 23 Multiple choice question. The number 3 is too small, and would result in a mean that is too low. Reason: 3 is not much different from most of the numbers. The number 23 is much larger than the other numbers and would unduly influence the mean. The number 4 is repeated three times, and would make the mean seem too close to 4.

Correct Answer The number 23 is much larger than the other numbers and would unduly influence the mean.

A statistic is: Multiple choice question. a characteristic of a population the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions a characteristic of a sample

Correct Answer a characteristic of a sample

What does a small value for a measure of dispersion tell us about a set of data? Multiple choice question. It indicates that the data is closely clustered around the center. It indicates that there are not very many values within the set of data. It shows that the values of the data are widely separated.

It indicates that the data is closely clustered around the center.

What does a measure of dispersion tell us about a set of data? Multiple choice question. It tells us the distance between adjacent values in the data. It tells us how fast the values change within the set of data. It describes the central tendency of the data. It tells us about the spread of the data.

It tells us about the spread of the data.

Most of the items sold at a garage sale cost about $12. Nothing sold for more than $15, but a few items cost only a few cents. What would be the best measure of the center of the distribution of sale prices? Multiple choice question. Median Mean Standard deviation Mode

Median

Most of the items sold at a garage sale cost about $12. Nothing sold for more than $15, but a few items cost only a few cents. What would be the best measure of the center of the distribution of sale prices? Multiple choice question. Mode Mean Median Standard deviation

Median

Question Mode Multiple Choice Question Which of the following statements best describes the strength of the range as a measure of dispersion? Multiple choice question. It does not provide information about how data are concentrated around the center of the distribution. Only two values from the data set are used. It may be unduly influenced by an especially small value. The calculation in easy to perform.

The calculation in easy to perform.

Which of the following accurately describes the median of a set of data? Multiple choice question. The midpoint of the data when it is arranged in order. The most numerous observation in a set of data. The arithmetic average of the values in the set. The difference in the largest and smallest values.

The midpoint of the data when it is arranged in order.

True or false: The variance is a measure of central tendency. True false question. True False

false

In a certain neighborhood most of the houses cost about $60,000. One house cost $700,000 and the mean cost was $82,500. The distribution of housing costs is: Multiple choice question. negatively skewed positively skewed symmetrical

positively skewed

which one of the following is true for a symmetrical distribution? Multiple choice question. The mean, median and mode all have the same value. The mode is the best choice of measure of location. The mean is less than the median. The mean is greater that the median.

Correct Answer The mean, median and mode all have the same value.

The mean, median, and mode are all the same for which type of distribution? Multiple choice question. A negatively skewed distribution. A positively skewed distribution. A symmetrical distribution.

Correct Answer A symmetrical distribution.

Which of the following statements best defines the mode? Multiple choice question. Any value that appears in the data more than once. The value that is the midpoint of the data. The value of the observation that appears most frequently. The arithmetic average of the data.

Correct Answer The value of the observation that appears most frequently.

What is the best measure of the center of an income distribution in a country where most of the households have annual incomes of about $40,000, but a small number of households have incomes above $1,000,000? Multiple choice question. Mode Median Mean Range

Median

The dispersion of a set of data is often referred to as which of the following? Multiple choice question. central tendency variation or spread measures of location

Correct Answer variation or spread

Which of the following statements are reasons to study the dispersion of data? Select all that apply. Multiple select question. A small value for dispersion indicates that the data is closely clustered around the center. It lets us compare the number of observations in two or more sets of data. It allows us to compare the spread in two or more distributions. It allows us to compare the central values of two or more distributions.

Correct Answer A small value for dispersion indicates that the data is closely clustered around the center. It allows us to compare the spread in two or more distributions.

Which of the following is an advantage of the mode? Multiple choice question. It is not affected by extreme values. Every data set has one value that is the mode. It is always equal to the median.

Correct Answer It is not affected by extreme values.

Which of the following are important properties of the arithmetic mean? Check all that apply. Multiple select question. All of the values in the data are used in calculating the mean. The mean can be calculated for nominal data. Σ(X-XX)=0 i.e. the sum of the deviations is zero. The mean is always less than the median. There is only one mean for a set of data.

Correct Answer All of the values in the data are used in calculating the mean. Σ(X-XX)=0 i.e. the sum of the deviations is zero. There is only one mean for a set of data.

Which of the following are disadvantages of the mode? Multiple select question. For many sets of data there is no mode. For many sets of data there are multiple modes. The mode is affected by extremely large and small values. Reason:This is a disadvantage of the mean. the mode can only be computed for interval-level data or higher Reason:The mode can be determined for all levels of data

Correct Answer For many sets of data there is no mode. For many sets of data there are multiple modes.

The formula for the weighted mean is Xw=Σ(wX)Σw Which of the following statements are true of the weighted mean? Select all that apply. Multiple select question. It gives a larger value for the mean than the formula for the arithmetic mean. It is a special case of the arithmetic mean. It is used when there are several observations of the same value. The denominator of the weighted mean is always the sum of the weights.

Correct Answer It is a special case of the arithmetic mean. It is used when there are several observations of the same value. The denominator of the weighted mean is always the sum of the weights. Need help? Review these concept resources.

Which of the following is an advantage of the mode? Multiple choice question. It is always equal to the median. It is not affected by extreme values. Every data set has one value that is the mode.

Correct Answer It is not affected by extreme values.

Which of the following kinds of data can be used to find a median value? Multiple select question. Ordinal level data Nominal level data Interval level data Ratio level data

Correct Answer Ordinal level data Interval level data Ratio level data

What does a small value for a measure of dispersion tell us about a set of data? Multiple choice question. It shows that the values of the data are widely separated. It indicates that the data is closely clustered around the center. It indicates that there are not very many values within the set of data.

It indicates that the data is closely clustered around the center.

Which of the following is true regarding medians and means? Multiple choice question. Means can be calculated from ratio-level data, but medians can't. Medians and means can be calculated from nominal-level data. Medians can be calculated from ordinal-level data, but means can't. Medians and means cannot calculated from interval-level data.

Correct Answer Medians can be calculated from ordinal-level data, but means can't.

Which of the following is true regarding medians and means? Multiple choice question. Medians can be calculated from ordinal-level data, but means can't. Medians and means can be calculated from nominal-level data. Reason:Neither can be calculated from nominal-level data. Medians and means cannot calculated from interval-level data. Reason:Both can be calculated from interval-level data. Means can be calculated from ratio-level data, but medians can't. Reason:Both can be calculated from ratio-level data.

Correct Answer Medians can be calculated from ordinal-level data, but means can't.

Which one of the following is true regarding the use of the mode, mean, and median for different levels of measurement? Multiple choice question. Only the mode can be used for nominal-level data. Only the mode can be used for ratio-level data. Only the mean and median can be used for ordinal-level data.

Correct Answer Only the mode can be used for nominal-level data.

For which of the following variables can one calculate a median? Multiple select question. Shoe size Species of flower Finishing position in a marathon (1st, 2nd, 3rd, ...) Color of cars at a car dealer Daily temperatures in August for the past 10 years

Correct Answer Shoe size Finishing position in a marathon (1st, 2nd, 3rd, ...) Daily temperatures in August for the past 10 years

For which of the following variables can one calculate an arithmetic mean? Multiple select question. Color of cars Daily temperatures in August for the past 10 years Time to run a marathon Finishing position in a marathon (1st, 2nd, 3rd, ...)

Correct Answer Daily temperatures in August for the past 10 years Time to run a marathon

Which of the following are reasons why the mode would not be a good choice of measure for the describing the center of a set of data? Check all that apply.

Correct Answer The data is bimodal. No observation occurs more than once. The most frequent observation is much higher or much lower than most of the data values.

The formula for the weighted mean is XXw=Σ(wX)ΣwΣ(wX)Σw Which of the following statements are true of the weighted mean? Select all that apply.

Correct Answer The denominator of the weighted mean is always the sum of the weights. It is used with data that has repeated values, such as a frequency distribution.

Which of the following is a population parameter if you are investigating the average age of patients at a local hospital? Multiple choice question. The ages of patients in the intensive care unit. The ages of patients on the third floor. The ages of all of the patients at a local hospital.

Correct Answer The ages of all of the patients at a local hospital.

How does the formula for the sample mean differ from the formula for population mean? Multiple choice question. For sample mean, the sum of values is divided by the number of values minus one. To calculate the sample mean, you divide by the sample number plus one. The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

Correct Answer The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).

Why would the median be a better measure of the center than the mean for the following set of data? 3, 4, 4, 4, 5, 6, 7, 23 Multiple choice question. The number 4 is repeated three times, and would make the mean seem too close to 4. The number 3 is too small, and would result in a mean that is too low. The number 23 is much larger than the other numbers and would unduly influence the mean.

Correct Answer The number 23 is much larger than the other numbers and would unduly influence the mean.

Select all that apply Which of the following are used to measure dispersion? Check all that apply. Average Standard Deviation Mean Range Variance Median

Correct Answer Standard Deviation Range Variance

How do you find the Population Mean for a set of data? Multiple choice question. Arrange the values in rank order and select the one in the middle. Sum the values in the population and then divide by the number of values in the population. Take the number of objects in the population and divide by the sum of all the values.

Correct Answer Sum the values in the population and then divide by the number of values in the population.

Which one of the following is true for a negatively skewed distribution? Multiple choice question. There are more observations above the mode than below it. There are more negative observations than positive observations. There are a small number of observations that are much lower in value than most of the data.

Correct Answer There are a small number of observations that are much lower in value than most of the data. Need help? Review these concept res

What characteristic of a data set makes the median the better measure of the center of the data than the mean? Multiple choice question. When the data set includes one or two very large or very small values. When the data set includes a very large number of observations. When the data set includes an evenly distributed set of values. When the data set includes one or two values that are repeated several times.

Correct Answer When the data set includes one or two very large or very small values.

The Population Mean is: Multiple choice question. the median value of the observations in the population the most common value in the population the arithmetic mean of all of the values in the population is pronounced "moo" (like the sound a cow makes)

Correct Answer the arithmetic mean of all of the values in the population

Which one of the following is a statistic? the average of a population Reason:This is a parameter. the mean of a sample the range of a population Reason:This is a parameter. the median of a population Reason:This is a parameter.

Correct Answer the mean of a sample

The median is defined as: Multiple choice question. the midpoint of the values after they have been arranged in rank order the value of the observation that occurs most frequently Reason: This is the Mode the arithmetic mean of the values of a set of data Reason: This is the Mean. the average of the largest and the smallest value in a data set Reason: This is referred to as the Midrange.

Correct Answer the midpoint of the values after they have been arranged in rank order

The median is defined as: Multiple choice question. the average of the largest and the smallest value in a data set Reason: This is referred to as the Midrange. the arithmetic mean of the values of a set of data Reason: This is the Mean. the midpoint of the values after they have been arranged in rank order the value of the observation that occurs most frequently Reason: This is the Mode

Correct Answer the midpoint of the values after they have been arranged in rank order

When you calculate the sample mean, you divide the sum of the values in the sample by Multiple choice question. the number of values in the sample. the sample number minus one. the number of non-repeating sample values.

Correct Answer the number of values in the sample.

The median would be a better measure for the center of the data for of which of the following data sets? Multiple choice question. {9, 11, 14, 16, 1, 12, 15, 17} {6, 6, 6, 7, 7, 8, 8, 8, 8, 9} {0.9, 1.2, 2.2, 1.6, 2.1, 3} {4, 6, 5, 8, 3, 4, 7, 5}

Correct Answer {9, 11, 14, 16, 1, 12, 15, 17}

Which of the following is the correct formula for the population variance? Multiple choice question. ΣX−μn−1ΣX-μn-1 Reason: This is not a valid statistics formula. Σ(X−μ)2NΣ(X-μ)2N Σ||X−μ||nΣ|X-μ|n Reason: This is the mean absolute deviation.

Correct Answer Σ(X−μ)2N